What verse are you referring to where God calls "them" Adam, in reference to Adam AND Eve? "Adam" is actually the generic term in the Hebrew, Babylonian and Asyrian languages for man. So Adam's name was literally"Man" which is exactly what he was and the first one to boot.
So it is possible, without looking at the verse you reference, that the term adam could be applied to the first man, or man as a collective species or creation- including womankind-therefore including Eve. This doesn't change Eve's name or who created her, it just lumps her in the same group as her husband, being adam. Am I close on this?
Smelly, the fact that God called both Adam and Eve, "man" does not mean that He did not make Eve. The whole of that verse says, "He created them male and female and blessed them. And when they were created He called them "man". (NIV) Also Genesis 1:27 and 2:22 make it clear that God created woman as well as man (as, indeed, He created every natural thing tha exists.)
Thank you for showing me the verse in question, Lynn. I did a cursory search on BG for verses using the term Adam, and that one didn't come up in the results for some reason. I got my info on the meaning of the name from one of the topical dictionaries on the site. I find it facinating that nearly all modern names are pulled directly from or are dirivitives of the names found in the OT. And we're reading the stories of the first individuals with those names. At the time, those names meant something, they decribed who that person was, and they were hand picked by God Himself. So cool.
Gen 5:1 This is the book of the generations of Adam. In the day that God created man, in the likeness of God made he him;
Gen 5:2 male and female created he them, and blessed them, and called their name Adam, in the day when they were created.
The first 9 words indicate that this is simply a historical recount of creation of Adam and his race similar to the begats found in Israels history- this recap simply shows what was already created.
Another thing to consider is that in the broader sense of the word Adam means not only man but mankind:
From the Websters Dictionary: AD'AM, n. In Heb., Man; primarily, the name of the human species, mankind; appropriately, the first Man, the progenitor of the human race. The word signifies form, shape, or suitable form, hence, species. It is evidently connected with Heb., to be like or equal, to form an image, to assimilate. Whence the sense of likeness, image, form, shape; Gr., a body, like. [See Man.]
Another thing to consider is at the moment of his creation Adam literally carried Eve's DNA in his rib so she was present in him.